Complete the rectangle to illustrate the product. (x+8)(x+7)
Sure! The answer to (x+8)(x+7) is... ta-daa! A beautiful rectangle with sides labeled (x+8) and (x+7). Now, just imagine the sheer beauty of a rectangle that encompasses all the mathematical wonders of this equation. It's truly a work of art!
To illustrate the product (x+8)(x+7), we can use the rectangle method.
Step 1: Draw a rectangle and label the sides with x+8 and x+7.
x+8
___________
| |
x+7| |
|___________|
Step 2: Divide the rectangle into four smaller rectangles.
x | 8
____|_____
x+7 | |
|___|
Step 3: Expand the sides of the rectangle.
x^2 + 7x
____|_____
x+7 | |
|___|
Step 4: Fill in the diagonals.
x^2 + 7x
____|_____
x+7 | 8 |
____|_____
| |
Step 5: Simplify the expression by combining like terms.
The complete rectangle shows the product (x+8)(x+7) as:
x^2 + 7x + 8x + 56
Simplifying further, we get:
x^2 + 15x + 56
To complete the rectangle and illustrate the product of (x+8)(x+7), we can use a visual method called the "box method" or "area model". This method involves creating a rectangle where the length and width represent the terms being multiplied.
Let's start by drawing a rectangle that represents (x+8) on the top and (x+7) on the side:
x 8
+--------+--------+
| | |
| | |
7 | | |
| | |
+--------+--------+
Next, divide the rectangle into four smaller sections by drawing vertical and horizontal lines. Each section of the rectangle represents a term that needs to be multiplied together:
x 8
+--------+--------+
| | |
| x | 8x |
7 | | |
| | |
+--------+--------+
The four sections are:
- Top-left: x * x = x^2
- Top-right: x * 8 = 8x
- Bottom-left: 7 * x = 7x
- Bottom-right: 7 * 8 = 56
Now, we have completed the rectangle and illustrated the product of (x+8)(x+7). The product can be obtained by summing up the values in each section:
(x+8)(x+7) = x^2 + 8x + 7x + 56
Simplifying the expression, we combine like terms:
(x+8)(x+7) = x^2 + 15x + 56
Therefore, the product of (x+8)(x+7) is x^2 + 15x + 56.